Lovelock black holes with maximally symmetric horizons

TL;DR

This paper explores properties of higher-dimensional Lovelock black holes with maximally symmetric horizons, classifies vacuum solutions, and derives thermodynamic laws for these black holes.

Contribution

It introduces a well-posed quasi-local mass in Lovelock gravity and classifies vacuum solutions, providing new insights into black hole thermodynamics in higher dimensions.

Findings

Classification of vacuum solutions into four types.

Proof of the first law of black-hole thermodynamics.

Expressions for heat capacity and free energy.

Abstract

We investigate some properties of n(\ge 4)-dimensional spacetimes having symmetries corresponding to the isometries of an (n-2)-dimensional maximally symmetric space in Lovelock gravity under the null or dominant energy condition. The well-posedness of the generalized Misner-Sharp quasi-local mass proposed in the past study is shown. Using this quasi-local mass, we clarify the basic properties of the dynamical black holes defined by a future outer trapping horizon under certain assumptions on the Lovelock coupling constants. The C^2 vacuum solutions are classified into four types: (i) Schwarzschild-Tangherlini-type solution; (ii) Nariai-type solution; (iii) special degenerate vacuum solution; (iv) exceptional vacuum solution. The conditions for the realization of the last two solutions are clarified. The Schwarzschild-Tangherlini-type solution is studied in detail. We prove the first law of black-hole thermodynamics and present the expressions for the heat capacity and the free energy.